I used to use my own domain for my personal e-mail. As it turned out, I wasn't using the domain for anything else, so I eventually decided to let the domain expire. Still, my personal e-mail needed to go somewhere... so I moved to Gmail.
In terms of general utility, Gmail is not that much different that having any other sort of web-based e-mail account -- I can check my mail from home or from work or from anywhere else I can get to the Internet.
Gmail gives me a gigabyte of storage for my e-mail messages, so I'm not encouraged to delete e-mails. I've been using Gmail since April 2004 and my space is only 15% full.
Messages in Gmail are also searchable, so I don't have to remember which labels I put on something in order to find old messages. I can search my e-mail easily and find things that might have taken a long time to track down by sorting and scrolling.
Labels, as opposed to folders, are a nice thing too. A message or conversation can have multiple labels associated with it, where most mail systems will only let a message live in one folder.
I see I've gone on longer than I intended, so I'll stop now. It's a neat-enough product, and a really cool web application, but if you have a mail system that works for you, feel free to stick with it.